7.19/7.14 MAYBE 7.19/7.14 7.19/7.14 DP problem for innermost termination. 7.19/7.14 P = 7.19/7.14 f9#(x1, x2) -> f1#(x1, x2) 7.19/7.14 f7#(I2, I3) -> f2#(I2, I3) 7.19/7.14 f2#(I4, I5) -> f7#(I4, rnd2) [0 <= -1 - I5 /\ y1 = y1 /\ y2 = -1 + y1 /\ 0 <= -1 - y2 /\ y3 = y3 /\ rnd2 = -1 + y3] 7.19/7.14 f6#(I6, I7) -> f2#(I6, I7) 7.19/7.14 f2#(I8, I9) -> f6#(I8, I10) [0 <= -1 - I9 /\ I11 = I11 /\ I12 = -1 + I11 /\ -1 * I12 <= 0 /\ 0 <= -1 + I12 /\ I13 = I13 /\ I10 = 1 + I13] 7.19/7.14 f5#(I14, I15) -> f2#(I14, I15) 7.19/7.14 f2#(I16, I17) -> f5#(I16, I18) [-1 * I17 <= 0 /\ 0 <= -1 + I17 /\ I19 = I19 /\ I20 = 1 + I19 /\ 0 <= -1 - I20 /\ I21 = I21 /\ I18 = -1 + I21] 7.19/7.14 f4#(I22, I23) -> f2#(I22, I23) 7.19/7.14 f2#(I24, I25) -> f4#(I24, I26) [-1 * I25 <= 0 /\ 0 <= -1 + I25 /\ I27 = I27 /\ I28 = 1 + I27 /\ -1 * I28 <= 0 /\ 0 <= -1 + I28 /\ I29 = I29 /\ I26 = 1 + I29] 7.19/7.14 f2#(I30, I31) -> f3#(I30, I32) [0 <= -1 - I31 /\ I33 = I33 /\ I32 = -1 + I33 /\ -1 * I32 <= 0 /\ I32 <= 0] 7.19/7.14 f2#(I34, I35) -> f3#(I34, I36) [-1 * I35 <= 0 /\ 0 <= -1 + I35 /\ I37 = I37 /\ I36 = 1 + I37 /\ -1 * I36 <= 0 /\ I36 <= 0] 7.19/7.14 f2#(I38, I39) -> f3#(I38, I39) [I39 <= 0 /\ -1 * I39 <= 0] 7.19/7.14 f1#(I40, I41) -> f2#(I40, I41) 7.19/7.14 R = 7.19/7.14 f9(x1, x2) -> f1(x1, x2) 7.19/7.14 f3(I0, I1) -> f8(rnd1, I1) [rnd1 = rnd1] 7.19/7.14 f7(I2, I3) -> f2(I2, I3) 7.19/7.14 f2(I4, I5) -> f7(I4, rnd2) [0 <= -1 - I5 /\ y1 = y1 /\ y2 = -1 + y1 /\ 0 <= -1 - y2 /\ y3 = y3 /\ rnd2 = -1 + y3] 7.19/7.14 f6(I6, I7) -> f2(I6, I7) 7.19/7.14 f2(I8, I9) -> f6(I8, I10) [0 <= -1 - I9 /\ I11 = I11 /\ I12 = -1 + I11 /\ -1 * I12 <= 0 /\ 0 <= -1 + I12 /\ I13 = I13 /\ I10 = 1 + I13] 7.19/7.14 f5(I14, I15) -> f2(I14, I15) 7.19/7.14 f2(I16, I17) -> f5(I16, I18) [-1 * I17 <= 0 /\ 0 <= -1 + I17 /\ I19 = I19 /\ I20 = 1 + I19 /\ 0 <= -1 - I20 /\ I21 = I21 /\ I18 = -1 + I21] 7.19/7.14 f4(I22, I23) -> f2(I22, I23) 7.19/7.14 f2(I24, I25) -> f4(I24, I26) [-1 * I25 <= 0 /\ 0 <= -1 + I25 /\ I27 = I27 /\ I28 = 1 + I27 /\ -1 * I28 <= 0 /\ 0 <= -1 + I28 /\ I29 = I29 /\ I26 = 1 + I29] 7.19/7.14 f2(I30, I31) -> f3(I30, I32) [0 <= -1 - I31 /\ I33 = I33 /\ I32 = -1 + I33 /\ -1 * I32 <= 0 /\ I32 <= 0] 7.19/7.14 f2(I34, I35) -> f3(I34, I36) [-1 * I35 <= 0 /\ 0 <= -1 + I35 /\ I37 = I37 /\ I36 = 1 + I37 /\ -1 * I36 <= 0 /\ I36 <= 0] 7.19/7.14 f2(I38, I39) -> f3(I38, I39) [I39 <= 0 /\ -1 * I39 <= 0] 7.19/7.14 f1(I40, I41) -> f2(I40, I41) 7.19/7.14 7.19/7.14 The dependency graph for this problem is: 7.19/7.14 0 -> 12 7.19/7.14 1 -> 2, 4, 6, 8, 9, 10, 11 7.19/7.14 2 -> 1 7.19/7.14 3 -> 2, 4, 6, 8, 9, 10, 11 7.19/7.14 4 -> 3 7.19/7.14 5 -> 2, 4, 6, 8, 9, 10, 11 7.19/7.14 6 -> 5 7.19/7.14 7 -> 2, 4, 6, 8, 9, 10, 11 7.19/7.14 8 -> 7 7.19/7.14 9 -> 7.19/7.14 10 -> 7.19/7.14 11 -> 7.19/7.14 12 -> 2, 4, 6, 8, 9, 10, 11 7.19/7.14 Where: 7.19/7.14 0) f9#(x1, x2) -> f1#(x1, x2) 7.19/7.14 1) f7#(I2, I3) -> f2#(I2, I3) 7.19/7.14 2) f2#(I4, I5) -> f7#(I4, rnd2) [0 <= -1 - I5 /\ y1 = y1 /\ y2 = -1 + y1 /\ 0 <= -1 - y2 /\ y3 = y3 /\ rnd2 = -1 + y3] 7.19/7.14 3) f6#(I6, I7) -> f2#(I6, I7) 7.19/7.14 4) f2#(I8, I9) -> f6#(I8, I10) [0 <= -1 - I9 /\ I11 = I11 /\ I12 = -1 + I11 /\ -1 * I12 <= 0 /\ 0 <= -1 + I12 /\ I13 = I13 /\ I10 = 1 + I13] 7.19/7.14 5) f5#(I14, I15) -> f2#(I14, I15) 7.19/7.14 6) f2#(I16, I17) -> f5#(I16, I18) [-1 * I17 <= 0 /\ 0 <= -1 + I17 /\ I19 = I19 /\ I20 = 1 + I19 /\ 0 <= -1 - I20 /\ I21 = I21 /\ I18 = -1 + I21] 7.19/7.14 7) f4#(I22, I23) -> f2#(I22, I23) 7.19/7.14 8) f2#(I24, I25) -> f4#(I24, I26) [-1 * I25 <= 0 /\ 0 <= -1 + I25 /\ I27 = I27 /\ I28 = 1 + I27 /\ -1 * I28 <= 0 /\ 0 <= -1 + I28 /\ I29 = I29 /\ I26 = 1 + I29] 7.19/7.14 9) f2#(I30, I31) -> f3#(I30, I32) [0 <= -1 - I31 /\ I33 = I33 /\ I32 = -1 + I33 /\ -1 * I32 <= 0 /\ I32 <= 0] 7.19/7.14 10) f2#(I34, I35) -> f3#(I34, I36) [-1 * I35 <= 0 /\ 0 <= -1 + I35 /\ I37 = I37 /\ I36 = 1 + I37 /\ -1 * I36 <= 0 /\ I36 <= 0] 7.19/7.14 11) f2#(I38, I39) -> f3#(I38, I39) [I39 <= 0 /\ -1 * I39 <= 0] 7.19/7.14 12) f1#(I40, I41) -> f2#(I40, I41) 7.19/7.14 7.19/7.14 We have the following SCCs. 7.19/7.14 { 1, 2, 3, 4, 5, 6, 7, 8 } 7.19/7.14 7.19/7.14 DP problem for innermost termination. 7.19/7.14 P = 7.19/7.14 f7#(I2, I3) -> f2#(I2, I3) 7.19/7.14 f2#(I4, I5) -> f7#(I4, rnd2) [0 <= -1 - I5 /\ y1 = y1 /\ y2 = -1 + y1 /\ 0 <= -1 - y2 /\ y3 = y3 /\ rnd2 = -1 + y3] 7.19/7.14 f6#(I6, I7) -> f2#(I6, I7) 7.19/7.14 f2#(I8, I9) -> f6#(I8, I10) [0 <= -1 - I9 /\ I11 = I11 /\ I12 = -1 + I11 /\ -1 * I12 <= 0 /\ 0 <= -1 + I12 /\ I13 = I13 /\ I10 = 1 + I13] 7.19/7.14 f5#(I14, I15) -> f2#(I14, I15) 7.19/7.14 f2#(I16, I17) -> f5#(I16, I18) [-1 * I17 <= 0 /\ 0 <= -1 + I17 /\ I19 = I19 /\ I20 = 1 + I19 /\ 0 <= -1 - I20 /\ I21 = I21 /\ I18 = -1 + I21] 7.19/7.14 f4#(I22, I23) -> f2#(I22, I23) 7.19/7.14 f2#(I24, I25) -> f4#(I24, I26) [-1 * I25 <= 0 /\ 0 <= -1 + I25 /\ I27 = I27 /\ I28 = 1 + I27 /\ -1 * I28 <= 0 /\ 0 <= -1 + I28 /\ I29 = I29 /\ I26 = 1 + I29] 7.19/7.14 R = 7.19/7.14 f9(x1, x2) -> f1(x1, x2) 7.19/7.14 f3(I0, I1) -> f8(rnd1, I1) [rnd1 = rnd1] 7.19/7.14 f7(I2, I3) -> f2(I2, I3) 7.19/7.14 f2(I4, I5) -> f7(I4, rnd2) [0 <= -1 - I5 /\ y1 = y1 /\ y2 = -1 + y1 /\ 0 <= -1 - y2 /\ y3 = y3 /\ rnd2 = -1 + y3] 7.19/7.14 f6(I6, I7) -> f2(I6, I7) 7.19/7.14 f2(I8, I9) -> f6(I8, I10) [0 <= -1 - I9 /\ I11 = I11 /\ I12 = -1 + I11 /\ -1 * I12 <= 0 /\ 0 <= -1 + I12 /\ I13 = I13 /\ I10 = 1 + I13] 7.19/7.14 f5(I14, I15) -> f2(I14, I15) 7.19/7.14 f2(I16, I17) -> f5(I16, I18) [-1 * I17 <= 0 /\ 0 <= -1 + I17 /\ I19 = I19 /\ I20 = 1 + I19 /\ 0 <= -1 - I20 /\ I21 = I21 /\ I18 = -1 + I21] 7.19/7.14 f4(I22, I23) -> f2(I22, I23) 7.19/7.14 f2(I24, I25) -> f4(I24, I26) [-1 * I25 <= 0 /\ 0 <= -1 + I25 /\ I27 = I27 /\ I28 = 1 + I27 /\ -1 * I28 <= 0 /\ 0 <= -1 + I28 /\ I29 = I29 /\ I26 = 1 + I29] 7.19/7.14 f2(I30, I31) -> f3(I30, I32) [0 <= -1 - I31 /\ I33 = I33 /\ I32 = -1 + I33 /\ -1 * I32 <= 0 /\ I32 <= 0] 7.19/7.14 f2(I34, I35) -> f3(I34, I36) [-1 * I35 <= 0 /\ 0 <= -1 + I35 /\ I37 = I37 /\ I36 = 1 + I37 /\ -1 * I36 <= 0 /\ I36 <= 0] 7.19/7.14 f2(I38, I39) -> f3(I38, I39) [I39 <= 0 /\ -1 * I39 <= 0] 7.19/7.14 f1(I40, I41) -> f2(I40, I41) 7.19/7.14 7.19/10.11 EOF